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Proof step 33 from proof abs-pos (previous step)

0 < j, 0 < j / gcd(i, j) ⊦ i = 0, j = 0, (abs(i) / gcd(i, j)) / gcd(abs(abs(i) / gcd(i, j)), abs(j / gcd(i, j))) = abs(i) / gcd(abs(i), j), abs(i) / gcd(i, j) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 34:
j ≠ 0 ⊦ abs(i / j) = abs(i) / abs(j)
Proof step 35:
gcd(i, j) ≠ 0, 0 < j, 0 < j / gcd(i, j) ⊦ i = 0, j = 0, (abs(i) / gcd(i, j)) / gcd(abs(abs(i) / gcd(i, j)), abs(j) / abs(gcd(i, j))) = abs(i) / gcd(abs(i), j), abs(i) / gcd(i, j) = 0

Rule argument

seq: j ≠ 0 ⊦ abs(i / j) = abs(i) / abs(j) subst: [j, i] → [gcd(i, j), j] rotate: F spec: int-div inst: name: abs

Additional information

Used simplifier rules: ⊦ gcd(i, j) = 0 ↔ i = 0 ∧ j = 0; Used terms: gcd(i, j), j